CENTRIFUGAL FORCE AND ELLIPTICITY BEHAVIOR OF A SLOWLY ROTATING ULTRA-COMPACT OBJECT

Using the optical reference geometry approach, we have derived a gener al expression for the ellipticity of a slowly rotating fluid configura tion using a Newtonian force balance equation in the conformally proje cted absolute 3-space,in the realm of general relativity. Further, wit h the help of the Hartle-Thorne (H-T) metric for a slowly rotating com pact object, we have evaluated the centrifugal force acting on a fluid element and also evaluated the ellipticity and found that the centrif ugal reversal occurs at around R/R(s) approximate to 1.45, and the ell ipticity maximum at around R/R(s) approximate to 2.75. The result has been compared with that of Chandrasekhar and Miller which was obtained in the full 4-spacetime formalism.